Question 84773: Can someone please help me with this type of word problems. thanks
Production Requirements An electronics company produces
transistors, resistors, and computer chips. Each transistor
requires 3 units of copper, 1 unit of zinc, and 2 units
of glass. Each resistor requires 3, 2, and 1 units of the three
materials, and each computer chip requires 2, 1, and 2 units
of these materials, respectively. How many of each product
can be made with the following amounts of materials?
a. 810 units of copper, 410 units of zinc, and 490 units
of glass
b. 765 units of copper, 385 units of zinc, and 470 units
of glass
c. 1010 units of copper, 500 units of zinc, and 610 units
of glass
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Production Requirements An electronics company produces
transistors, resistors, and computer chips. Each transistor
requires 3 units of copper, 1 unit of zinc, and 2 units
of glass. Each resistor requires 3, 2, and 1 units of the three
materials, and each computer chip requires 2, 1, and 2 units
of these materials, respectively. How many of each product
can be made with the following amounts of materials?
:
Let x = no. transistors
Let y = no. of resistors
Let z = no. of chips
:
a. 810 units of copper, 410 units of zinc, and 490 units of glass
Write an equation for each material:
Copper: 3x + 3y + 2z = 810
Zinc: 1x + 2y + 1z = 410
Glass: 2x + 1y + 2z = 490
:
A convenient thing happens if we multiply the 1st equation by -1 and add all 3:
-3x - 3y - 2z = -810
1x + 2y + 1z = 410
2x + 1y + 2z = 490
-----------------------adding eliminates x & y
0x + 0y + 1z = +90 each chips can be made
:
Substitute 90 for z in the zinc and glass equations and you have;
1x + 2y + 90 = 410 >> 1x + 2y = 320
2x + 1y +180 = 490 >> 2x + 1y = 310
:
Multiply the 1st equation by 2 and subtract the 2nd equation:
2x + 4y = 640
2x + 1y = 310
--------------subtracting eliminates x:
0x + 3y = 330
y = 330/3
y = 110 ea resistors
:
Find x using x + 2y = 320, substitute 110 for y
x + 220 = 320
x = 320 - 220
x = 100 ea transistors
:
b. 765 units of copper, 385 units of zinc, and 470 units of glass
:
Copper: 3x + 3y + 2z = 765
Zinc: 1x + 2y + 1z = 385
Glass: 2x + 1y + 2z = 470
:
Follow exactly the same procedure as we did in the 'a' part using the above equations
notice that only the last value in the equation will change.
c. 1010 units of copper, 500 units of zinc, and 610 units of glass
:
Copper: 3x + 3y + 2z = 1010
Zinc: 1x + 2y + 1z = 500
Glass: 2x + 1y + 2z = 610
:
Do the same here.
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